01 Dakota Serpentine belt comes off - I'm Stuck
 

The serpentine belt kept crawling off the A/C pulley. I replaced the tensioner pulley but it didn't help. I put a shorter belt on to bypass the A/C pulley and it still crawls off power steering pulley and shreds the edge of the belt. I pulled the power steering pulley in and out by hand and saw there is a little play. Is that the problem and will it take a new power steering unit to fix it?

If the pulley moves on the shaft, then the shaft is moving inside the pump. Yes, your pump is toast. You could possibly rebuild it, but it would be cheaper to get a new one, emphasis on new. Part store "rebuilds" are someone else's worn out pump that's been dipped in cleaner that's now illegal in the US, and... that's it. You'd only come out ahead if the pump you get is one that someone else replaced by mistake. If a new one is no longer available, try for a Mopar or NAPA gold rebuild. At least they're actually rebuilt. You can also call around to your local hydraulic shops and see if anyone local to you can rebuild it.

When mine did that, the power steering pump pulley cam off in my hand, along with the shaft it was mounted on, when I took the belt off.......